Method of determining a route minimizing the energy consumption of a vehicle using a line graph

ABSTRACT

The present invention relates to a method of determining a route (ITI) minimizing the energy consumption of a vehicle, based on the use of a dynamic model (MOD) of the vehicle depending on the vehicle speed and acceleration, the construction of a line graph (GA) and a shortest path algorithm (ALG) suited for negative energies.

FIELD OF THE INVENTION

The present invention relates to the field of vehicle navigation and inparticular to the field of eco-routing, which determines a routeminimizing the energy consumption of a vehicle for a given route.

BACKGROUND OF THE INVENTION

According to the International Energy Agency, more than 50% of thepetroleum consumed worldwide is used by the transport sector, more thanthree quarters of which for road transport. Again, according to thisagency, the transport sector is responsible for around a quarter (23.8%)of greenhouse gas emissions and for more than a quarter (27.9%) of CO₂emissions in Europe in 2006.

It is therefore more important than ever to increase the energyefficiency of road travels in order to reduce the consumption of energy,whether fossil or electrical energy. Thus, Advanced Driver AssistanceSystems (ADAS) represent a promising solution, both economical (thedriver's smartphone can simply be used) and non-intrusive (themechanical components of the vehicle require no modifications).

Among the driver assistance systems intended to improve the energyefficiency of driving techniques, there are mainly two strategies thancan and should be complementary: eco-driving and eco-routing.Eco-driving consists in optimizing, in terms of energy consumption, aspeed profile along a route. This speed profile is then suggested to thedriver, who can reduce the consumption during the ride by following therecommended route. An example of a method concerning eco-driving isdescribed in patent application FR-2,994,923 (U.S. Pat. No. 9,286,737).Eco-routing consists in identifying the optimum route to go from a startpoint to an end point by minimizing the energy consumption, and bytaking account of a multiplicity of parameters such as thecharacteristics of the vehicle, the topological characteristics of theroad network, the traffic conditions, etc.

Eco-routing is considered in the following patent applications:US-2012/123,657, US-2012/179,315, US-2012/066,232, U.S. Pat. No.9,091,560. However, these patent applications do not specify how theroute minimizing the energy consumption is determined or how the speedused for these methods is determined. It is therefore not possible toknow the precision obtained by the methods described in these patentapplications.

Other eco-routing methods are based on Dijkstra's shortest pathalgorithm for determining the route minimizing the energy consumption.However, this algorithm does not take negative values into account.Therefore, this algorithm can be used only for combustion enginevehicles, and it cannot be used for electric vehicles for which energyrecovery is possible (with regenerative braking for example). Thesemethods are consequently not adaptable to any type of vehicle. Suchmethods are notably described in the following documents:

-   Andersen O, Jens C S, Torp K, Yang B (2013), « EcoTour: Reducing the    environmental footprint of vehicles using eco-routes », Proc. 2013    IEEE 14th Int. Conf. on Mobile Data Management, Milan, Italy, 3-6    Jun. 2013,-   Boriboonsomsin K, Barth M J, Zhu W, Vu A (2012), « Eco-routing    navigation system based on multisource historical and real-time    traffic information », IEEE Trans. on Intelligent Transportation    Systems, vol. 13, no. 4, p. 1694-1704,-   Ben Dhaou I, « Fuel estimation model for ECO-driving and ECO-routing    », Proc. 2011 IEEE Intelligent Vehicles Symposium, Baden-Baden,    Germany, 5-9 Jun. 2011, p. 37-42,-   Ericsson E, Larsson H, Brundell-Freij K (2006), « Optimizing route    choice for lowest fuel consumption—Potential effects of a new driver    support tool », Transportation research Part C, vol. 14, p. 369-383.

In order to overcome these drawbacks, the present invention relates to amethod of determining a route minimizing the energy consumption of avehicle, based on the use of a dynamic model of the vehicle depending onthe vehicle speed and acceleration, the construction of a line graph anda shortest path algorithm suited for negative energies. Using such adynamic model and constructing a line graph allows higher energyconsumption precision, notably by taking account of the accelerations.The algorithm suited for negative energies makes the method adaptable toany type of vehicle, including electric vehicles.

SUMMARY OF THE INVENTION

The invention thus relates to a method of determining a route minimizingthe energy consumption of a vehicle travelling on a road network. Forthis method, the following steps are carried out:

a) identifying the position and the destination of said vehicle,

b) constructing a dynamic model of said vehicle that relates the energyconsumed by said vehicle to the speed and the acceleration of saidvehicle,

c) constructing a line graph of said road network between saididentified position of said vehicle and said identified destination ofsaid vehicle,

d) determining the energy consumed by said vehicle for each arc of saidline graph by means of said dynamic model of the vehicle and of anaverage speed of said vehicle on said considered arc, and of anacceleration of said vehicle to reach said average speed on saidconsidered arc,

e) determining said route between said identified position of saidvehicle and said identified destination of said vehicle by means of ashortest path algorithm minimizing on said line graph said energyconsumption, said shortest path algorithm being suited to take intoaccount, where appropriate, a negative energy consumption on at leastone arc of said line graph.

According to an embodiment, said average speed and said acceleration ofsaid vehicle are determined by means of traffic conditions and/or of thetopology and/or of the infrastructures of said road network.

According to a variant, said traffic conditions are obtained in realtime through communication with online data services.

Alternatively, said traffic conditions are stored in historical datastorage means.

According to a feature, said line graph is constructed using thetopology of said road network.

According to an implementation option, said topology of said roadnetwork is determined using geolocation means.

According to an embodiment, said dynamic model of the vehicle depends onintrinsic parameters of said vehicle.

Preferably, said intrinsic parameters of said vehicle are obtained froma database or they are transmitted by a user.

According to an embodiment, said route is displayed on an autonomousdevice or on the dashboard of said vehicle.

Advantageously, said dynamic model of said vehicle depends on the powerrequest of at least one auxiliary system of said vehicle.

Preferably, said power request of at least one auxiliary system dependson the outside temperature.

According to an embodiment, said shortest path algorithm is aBellman-Ford algorithm.

According to a variant embodiment, said line graph is constructed bycarrying out the following steps:

i) constructing a directed graph (GD) of said road network (RR) withnodes (N) and arcs (A), said nodes (N) of said directed graph (GD)corresponding to the intersections of said road network, and said arcs(A) of said directed graph corresponding to the roads connecting saidintersections, and

ii) constructing said line graph (GA) of said road network (RR) withnodes (N) and arcs (A), said nodes (N) of said line graph (GA)corresponding to the arcs (A) of said directed graph (GD) and said arcs(A) of said line graph (GA) corresponding to the adjacency of said arcs(A) of said directed graph (GD).

Besides, the invention relates to a computer program productdownloadable from a communication network and/or recorded on acomputer-readable medium and/or processor or server executable,comprising program code instructions for implementing the methodaccording to one of the above features, when said program is executed ona computer or on a mobile phone.

BRIEF DESCRIPTION OF THE FIGURES

Other features and advantages of the method according to the inventionwill be clear from reading the description hereafter of embodimentsgiven by way of non-limitative examples, with reference to theaccompanying figures wherein:

FIG. 1 illustrates the steps of the method according to an embodiment ofthe invention,

FIG. 2 illustrates the steps of the method according to a secondembodiment of the invention,

FIG. 3 illustrates the construction of a line graph according to anembodiment of the invention,

FIG. 4 illustrates the average speed and the measured speeds over afirst path,

FIG. 5 illustrates the cumulative measured energy consumption, thecumulative energy consumption determined by a model according to theprior art and the cumulative energy consumption determined by a dynamicmodel according to the invention, for the example of FIG. 4,

FIG. 6 illustrates the average speed and the measured speeds for asecond path, and

FIG. 7 illustrates the cumulative measured energy consumption, thecumulative energy consumption determined by a model according to theprior art and the cumulative energy consumption determined by a dynamicmodel according to the invention, for the example of FIG. 6.

DETAILED DESCRIPTION OF THE INVENTION

The present invention relates to an eco-routing method, i.e. a method ofdetermining a route minimizing the energy consumption of a vehicletravelling on a road network. A route is understood to be the path thatshould be traveled by a vehicle in order to go from a start point(current position of the vehicle) to an end point (destination of thevehicle).

The method according to the invention is suited to any type of vehicle:combustion vehicles, hybrid vehicles, electric vehicles.

Notations

The following notations are used in the description hereafter:

v Vehicle speed [m/s] x Vehicle position [m] m Vehicle mass [kg] ωVehicle engine speed [tr/s] F_(w) Vehicle traction force on the wheel[N] F_(areo) Aerodynamic force on the vehicle [N] F_(friction) Frictionforce undergone by the vehicle [N] F_(slope) Normal force undergone bythe vehicle (gravity) [N] F_(res) Resultant of aerodynamic and rollinglosses [N] α Angle of inclination of the road [rad] ρ_(a) Air density[kg/m³] A_(f) Frontal area of the vehicle [m2] c_(d) Aerodynamic dragcoefficient [—] c_(r) Rolling resistance coefficient [—] g Gravitationalacceleration [m²/s] a₀, a₁ and a₂ Vehicle parameters [—] r Wheel radius[m] ρ_(t) Vehicle transmission ratio [—] η_(t) Vehicle transmissionefficiency [—] T_(m) Engine torque [Nm] T_(m,max) Maximum engine torque[Nm] T_(m,min) Minimum engine torque [Nm] P_(m) Power available atengine shaft [W] P_(b) Power demand at the battery [W] η_(b) Aggregateefficiency of the electric traction chain [—] P_(aux) Power of thevehicle auxiliaries [W] T_(amb) Ambient temperature [K] i Road segment i[—] i-1 Road segment preceding road segment i [—] ν Average trafficspeed [m/s] K Function Ē_(i) Energy consumption over segment i [Wh]E_(b) Energy consumption at the battery [Wh] P _(i) Power of the vehicleon segment i at average speed [W] {tilde over (P)}_(i) Power of thevehicle on segment i at variable speed [W] T_(i) Travel time on segmenti [s] l_(i) Length of segment i [m] E_(jump,i) Energy consumptionassociated with speed fluctuation for segment i [Wh] t_(jump,i) Timerequired for speed fluctuation for segment i [s] W_(k)* Line graph arcweight [Wh]

For these notations, the time derivative is denoted by

$\frac{d}{dt}$

or by a point above the variable considered.

The method according to the invention comprises the following steps:

1) vehicle position and destination identification

2) vehicle dynamic model construction

3) line graph construction

4) energy consumption determination on the line graph

5) route determination.

The dynamic model construction and line graph construction steps can becarried out in this order, simultaneously or in the reverse order.

FIG. 1 illustrates by way of non-limitative example the steps of themethod according to an embodiment of the invention.

1) vehicle position and destination identification (D/A)

2) vehicle dynamic model construction (MOD)

3) line graph construction (GA)

4) energy consumption determination on the line graph, using the dynamicmodel (MOD) and the line graph (GA)

5) eco-route (ITI) determination by means of a shortest path algorithm(ALG) applied to the line graph (GA) weighted by the energy consumption.

FIG. 2 illustrates by way of non-limitative example the steps of themethod according to a second embodiment of the invention. In addition tothe steps described in connection with FIG. 1, the method comprises thefollowing optional steps:

determining the road network topology (TOP), the road network topologycan be used for construction of the dynamic model (MOD) and forconstruction of the line graph (GA),

determining the road traffic (TRA), traffic determination can be usedfor construction of the dynamic model (MOD) and for construction of theline graph (GA),

determining the intrinsic parameters of the vehicle (PAR), theseparameters can be used for construction of the dynamic model (MOD),

constructing a directed graph (GD) of the road network, the directedgraph can be obtained using the road network topology (TOP) and it canbe used for construction of the line graph (GA).

The steps of determining the road network topology (TOP), the roadtraffic (TRA) and the intrinsic parameters of the vehicle (PAR) areindependent. It is therefore possible to carry out only part of thesesteps.

All the steps of the method, including their variants shown in FIG. 2,are described below.

1) Vehicle Position and Destination Identification

In this step, the current position and the destination of the vehicleare identified. In other words, the start point and the end point of theroute to be traveled are identified.

The current position of the vehicle can be identified using ageolocation system (of GPS or Galileo type for example). Alternatively,the current position can be given by a user using an interface therewith(a smartphone, the dashboard or a geolocation system for example).

The destination of the vehicle can be given by a user using an interfacetherewith. Alternatively, the destination can be stored in a database,for example if it is a previously known destination (a smartphone, thedashboard or a geolocation system for example).

2) Vehicle Dynamic Model Construction

In this step, a dynamic model of the vehicle is constructed. What isreferred to as dynamic model of the vehicle is a model connecting theenergy consumption of the vehicle to the speed and acceleration of thevehicle. The dynamic model of the vehicle can be constructed using thefundamental principle of dynamics, associated with an engine energymodel.

According to an embodiment of the invention (see the step of determiningthe intrinsic parameters of the vehicle of FIG. 2), the model can beconstructed from macroscopic parameters of the vehicle, for example:vehicle engine power, vehicle mass, maximum power, maximum speed,transmission type, aerodynamic parameters, etc. Thus, the dynamic modelis representative of the vehicle and it takes account of its specificcharacteristics.

According to a variant embodiment, the macroscopic parameters can beobtained from a database that lists the various vehicles in service. Forexample, the macroscopic parameters can be obtained by entering theregistration number of the vehicle, the database associating the platenumber with the design thereof (make, model, engine power, etc.) andcomprising the macroscopic parameters of the vehicle. Alternatively, themacroscopic parameters can be manufacturer data provided by the user, inparticular using an interface (a smartphone, the dashboard or ageolocation system for example).

The dynamic model of the vehicle can also depend on road parameters suchas the slope of the road. Such data can be obtained from a topology (seethe topology determination step of FIG. 2) or a map of the road network.

The dynamic model of the vehicle takes account of the dynamics of thevehicle. It can be constructed from the application of the fundamentalprinciple of the vehicle dynamics applied to the longitudinal axisthereof, and it can be written as follows:

${m\frac{{dv}(t)}{dt}} = {F_{w} - F_{aero} - F_{friction} - F_{slope}}$

where m is the mass of the vehicle, v(t) the speed thereof, F_(w) theforce on the wheel, F_(aero) the aerodynamic force, F_(friction) therolling resistance force and F_(slops) the gravitational force. Themodel can thus be rewritten as follows:

$\quad\left\{ \begin{matrix}{{\overset{.}{x}(t)} = {v(t)}} \\{{m{\overset{.}{v}(t)}} = {F_{w} - {\frac{1}{2}\rho_{a}A_{f}c_{d}{v(t)}^{2}} - {mgc}_{r} - {{mg}\; {\sin \left( {a(x)} \right)}}}}\end{matrix} \right.$

where ρ_(a) is the air density, A_(f) the frontal area of the vehicle,c_(d) the aerodynamic drag coefficient, c_(r) the rolling resistancecoefficient, α(x) the slope of the road as a function of the positionand g the gravitational acceleration. The sum of the aerodynamic androlling losses is generally approximated with a second-order polynomialas a function of speed v:

F _(reS) =F _(aero) +F _(friction) =a ₂ v(t)² +a ₁ v(t)+a ₀

where parameters a₀, a₁ and a₂ can be identified for the vehicleconsidered from a standard test referred to as coast down test.

Therefore, the force on the wheel can be expressed as follows:

F _(w) =m{dot over (v)}(t)+a ₂ v(t)² +a ₁ v(t)+a ₀ +mg sin(α(x))

Hereafter, the dynamic model of the vehicle is described for anon-limitative embodiment of an electric vehicle. The electric vehiclecomprises at least one electric machine, at least one electric energystorage means (such as a battery) for powering the electric motor or forbeing powered by the electric machine (in case of regenerative braking),and energy recovery means, notably regenerative braking means. However,the model is adaptable to any type of engine (thermal, hybrid,electric).

The torque requested from the electric machine to achieve the requestedforce on the wheel is defined as follows:

$T_{m} = \left\{ \begin{matrix}{\frac{F_{w}r}{\rho_{t}\eta_{t}},} & {{{if}\mspace{14mu} F_{w}} \geq 0} \\{\frac{F_{w}r\; \eta_{t}}{\rho_{t}},} & {{{if}{\mspace{11mu} \;}F_{w}} < 0}\end{matrix} \right.$

where r is the radius of the wheel, ρ_(t) and η_(t) are the transmissionratio and the transmission efficiency. An electric machine is generallya reversible machine, therefore it behaves like a motor when T_(m) ispositive and like a generator (energy recovery) when T_(m) is negative.The torque generated by the electric machine is saturated by T_(m,max)and T_(m,min). In particular, during braking phases, if the enginetorque is less negative than saturation value T_(m,min), then thevehicle is slowed down only by the regenerative braking system.Otherwise, the mechanical brake comes into operation, thus adding itsaction to the regenerative braking.

The power available at the engine shaft, in the presence of aregenerative braking system, can be defined as follows:

$P_{m} = \left\{ \begin{matrix}{{T_{m,\max}{\omega (t)}},} & {{{if}\mspace{14mu} T_{m}} \geq T_{m,\max}} \\{{T_{m}{\omega (t)}},} & {{{if}\mspace{14mu} T_{m,\min}} < T_{m} < T_{m,\max}} \\{{T_{m,\min}{\omega (t)}},} & {{{if}\mspace{14mu} T_{m}} \leq T_{m,\min}}\end{matrix} \right.$

where ω_(t) is the engine speed defined as:

${\omega (t)} = \frac{{v(t)}\rho_{t}}{r}$

The power demand at the battery is expressed as follows:

$P_{b} = \left\{ \begin{matrix}{\frac{P_{m}}{\eta_{b}},} & {{{if}\mspace{14mu} P_{m}} \geq 0} \\{{P_{m}\eta_{b}},} & {{{if}\mspace{14mu} P_{m}} < 0}\end{matrix} \right.$

where η_(b) is the aggregate efficiency of the electric traction chain(inverter, battery, etc.).

According to an embodiment of the invention, the precision of the modeland of the estimation of the energy consumption of a path can beimproved by taking account of the power demand of at least one auxiliarysystem in the dynamic model of the vehicle. Indeed, the power requestedby the driver for comfort purposes, notably for passenger compartmentheating or air conditioning, is particularly costly in terms of energyconsumption, notably for an electric vehicle where heating can have avery strong impact on the range. The term relative to the powerrequested by the auxiliaries can be expressed as a function of theambient temperature:

P _(aux) =K(T _(amb))

Thus, for this embodiment, the energy consumption at the battery over atime horizon T can be defined as:

E _(b)=∫₀ ^(T) +P _(b) +P _(aux) dt

The model described above requires an instantaneous speed signal. Thisinformation is not available a priori on the road segments (roadportions of the road network) for which the only information availableare average speeds.

According to the invention, an average speed is first considered foreach road segment, then the vehicle acceleration to reach this averagespeed from the previous segment is considered. Preferably, the averagespeed can be obtained from information on the road traffic on the roadnetwork.

According to a variant, the average speed on a segment can be obtainedin real time through communication with online data services thatacquire real-time information on the traffic on the road network. Thisoptional traffic determination step is described for the embodiment ofFIG. 2.

Alternatively, the average speed can be stored by historical datastorage means that store traffic data relative to the road network,notably for different days, different times, etc.

Thus, if the average speed v due to the traffic on a road segment isassumed to be known, the model described above can be modified in orderto assess the energy consumption of the vehicle for travelling the roadsegment considered. Speed v(t) is subsequently replaced by the averagetraffic speed v in the dynamic model. It is thus assumed that all thevehicles on road segment i run at speed v _(i). The expression of theforce on the wheel is therefore modified for each road segment i;

F _(w,i) =a ₂ v _(i) +a ₁ v _(i) +a ₀ +mg sin(α_(i)(x))

where the acceleration term disappears. The engine torque becomes:

${\overset{\_}{T}}_{m,i} = \left\{ \begin{matrix}{\frac{{\overset{\_}{F}}_{w,i}r}{\rho_{t}\eta_{t}},} & {{{if}\mspace{14mu} {\overset{\_}{F}}_{w,i}} \geq 0} \\{\frac{{\overset{\_}{F}}_{w,i}r\; \eta_{t}}{\rho_{t}},} & {{{if}\mspace{11mu} {\overset{\_}{\; F}}_{w,i}} < 0}\end{matrix} \right.$

The engine speed is also constant over time since a constant speed v_(t) is assumed:

${\overset{\_}{\omega}}_{i} = \frac{{\overset{\_}{v}}_{i}\rho_{t}}{r}$

The mechanical power available at the electric machine is rewritten asfollows:

${\overset{\_}{P}}_{m,i} = \left\{ \begin{matrix}{{T_{m,\max} \cdot {\overset{\_}{\omega}}_{i}},} & {{{if}\mspace{14mu} T_{m,i}} \geq T_{m,\max}} \\{{{\overset{\_}{T}}_{m,i} \cdot {\overset{\_}{\omega}}_{i}},} & {{{if}\mspace{14mu} T_{m,\min}} < {\overset{\_}{T}}_{m,i} < T_{m,\max}} \\{{T_{m,\min} \cdot {\overset{\_}{\omega}}_{i}},} & {{{if}\mspace{14mu} {\overset{\_}{T}}_{m,i}} \leq T_{m,\min}}\end{matrix} \right.$

It is assumed hereafter that the torque saturation values areindependent of the engine speed. However, other embodiments are valid,notably the maximum and minimum torques can depend on the engine speed.

The power request from the battery of the electric vehicle can bedefined as follows:

${\overset{\_}{P}}_{b,i} = \left\{ \begin{matrix}{\frac{{\overset{\_}{P}}_{m,i}}{\eta_{b}},} & {{{if}\mspace{14mu} {\overset{\_}{P}}_{m,i}} \geq 0} \\{{{\overset{\_}{P}}_{m,i}\eta_{b}},} & {{{if}\mspace{14mu} {\overset{\_}{P}}_{m,i}} < 0}\end{matrix} \right.$

The energy consumption of the battery thus is:

Ē _(b,i)=( P _(b,i) +P _(aux))T _(i)

where T_(i)=l_(i)/v _(i) is the travel time on road segment i if thevehicle runs at the average traffic speed v _(i).

Using the average speed in energy consumption models is a standardapproach in the prior art. The method according to the inventionproposes to take account of the acceleration in the dynamic model of thevehicle for a more precise and reliable assessment of the trueconsumption. To take acceleration phenomena into account, the travelover each road segment is divided into two phases: a phase of constantcruising speed v _(t) and a speed fluctuation (i.e. acceleration ordeceleration) phase for switching from speed v _(i-1), i.e. the averagespeed of the previous segment, to speed v _(i), i.e. the average speedof the current segment. Preferably, a constant acceleration (ordeceleration) is considered to reach speed v _(i). Therefore, even ifthe available macroscopic information does not allow to know thetemporal information, the spatial acceleration occurring at theinterface between two road segments is considered. The energyconsumption E_(jump,i) associated with the speed fluctuation between tworoad segments is defined as follows:

$E_{{jump},i} = {\int_{0}^{t_{{jump},i}}{\left( {{\overset{\sim}{P}}_{b,i} + P_{aux}} \right){dt}}}$

with {tilde over (P)}_(b,i) the power demand at the battery for theacceleration phase to shift from speed v_(i-1) to speed v_(i).

Such a power demand at the battery can be obtained, as previouslystated, from a force on the interface wheel defined as:

{tilde over (F)} _(w) =m·a+a ₂ v(t)² +a ₁ v(t)+a ₀

where the time-varying speed v(t) in each transient can here be linearlymodelled as follows:

v(t)=v _(i-1)+sign(v _(i) −v _(i-1))·a·t

where v _(i-1) the speed on the upstream segment, v _(i) is the speed onthe downstream segment and a is the constant acceleration for achievingthe speed change. The speed fluctuation is thus achieved as follows:

$t_{{jump},i} = \frac{{\overset{\_}{v}}_{i} - {\overset{\_}{v}}_{i - 1}}{{{sign}\left( {{\overset{\_}{v}}_{i} - {\overset{\_}{v}}_{i - 1}} \right)} \cdot a}$

The total energy consumption on segment t is thus defined:

E _(b,i) =E _(b,i) +E _(jump,i)

Taking the interface accelerations into account makes the model moreprecise. However, the a priori available information is not alwayscomplete or updated. Notably, it is not probable to have preciseinformation on the average traffic speeds for secondary roads. It istherefore possible to have long road portions for which the trafficspeed is simply a constant nominal value. In this case, taking intoaccount only the data relative to the road network would consist inassuming that there is no acceleration, which would generate big energyconsumption assessment errors. That is why the invention also allows toenrich the road network-related data by integrating the speedperturbations induced by critical elements of the road infrastructure,notably traffic lights, intersections and bends. For example, if atraffic light is known to be located at the interface between twosegments, its impact is taken into account in the consumptionassessment, by taking account of the speed fluctuation between the twosegments.

Taking account of these accelerations not only allows to obtain morerealistic and precise energy costs, but also to avoid negative loops inthe routing graph modelling the road network. Indeed, the negative looprepresents a sequence of road segments having the same start and endpoint with a negative total cost. In the specific case of a weightedgraph with energy weights, this represents a situation of infiniteenergy recovery when travelling the loop continuously, which is inactual fact impossible. This criticality is easily verified whenconsidering electric vehicles and if the consumption assessment for aroad segment and neighbouring segments does not take account ofimportant elements such as the slope and/or the accelerations fortransiting from one segment to another. The presence of negative loopsin the routing graph prevents from finding a route that globallyminimizes the consumption because the search algorithm would convergetrivially on these loops to reduce the consumption.

According to an embodiment of the invention, the speed fluctuationbetween the two segments can be modelled as two transients: the firstone for changing from speed v _(i-1) to 0 (for stopping at a trafficlight for example) and the second for changing from speed 0 to speedv_(i). Thus, the energy consumption related to the speed fluctuation canbe described as the sum of two contributions:

$E_{{jump},i} = {{\int_{0}^{t_{{{jump}\; 1},i}}{\left( {{\overset{\sim}{P}}_{{b\; 1},i} + P_{aux}} \right){dt}}} + {\int_{0}^{t_{{{jump}\; 2},i}}{\left( {{\overset{\sim}{P}}_{{b\; 2},i} + P_{aux}} \right){dt}}}}$

where the speed fluctuation in the first term is modelled as follows:

v _(i)(t)= v _(i-1) −a·t

and the time required for the first fluctuation:

t _(jump,i) =v _(i-1) /a

Similarly, the speed fluctuation in the second term is modelled asfollows:

v ₂(t)=a·t

and the time required for this fluctuation:

t _(jump2,i) =v _(i) /a

Therefore, according to the invention, the dynamic model of the vehiclecan be written (for any type of vehicle):

$E_{i} = {{{\overset{\_}{P}}_{i}T_{i}} + {\int_{0}^{t_{{jump},i}}{{\overset{\sim}{P}}_{i}{dt}}}}$

with E_(i) the energy consumption on segment i, P _(i) the powerrequested from the energy storage system of the vehicle (fuel tank,battery, etc.) when the vehicle is considered to be at constant speed onsegment i, T_(i) the time during which the vehicle is considered to beat constant speed on segment i, {tilde over (P)}_(i) the power requestedfrom the energy storage system of the vehicle when the vehicle isconsidered to have a speed fluctuation (speed fluctuation betweensegment i−1 and segment i), and t_(jump,i) the time required forachieving the speed fluctuation. The first term of the model correspondsto the energy consumption on the segment due to the average speed andthe second term corresponds to the energy consumption due to the speedfluctuation for reaching the average speed.

For the embodiment taking into account the power demand of at least oneauxiliary system, the dynamic model of the vehicle can be written asfollows (for any type of vehicle):

$E_{i} = {{\left( {{\overset{\_}{P}}_{i} + P_{aux}} \right)T_{i}} + {\int_{0}^{t_{{jump},i}}{\left( {{\overset{\sim}{P}}_{i} + P_{aux}} \right){dt}}}}$

with E_(i) the energy consumption on segment i, P _(i) the powerrequested from the energy storage system of the vehicle (fuel tank,battery, etc.) when the vehicle is considered to be at constant speed onsegment i, P_(aux) the power demand of at least one auxiliary system,T_(i) the time during which the vehicle is considered to be at constantspeed on segment i, {tilde over (P)}_(i) the power requested from theenergy storage system of the vehicle when the vehicle is considered tohave a speed fluctuation (speed fluctuation between segment i−1 andsegment i), and L_(jump,i) the time required for achieving the speedfluctuation. The first term of the model corresponds to the energyconsumption on the segment due to the average speed and the second termcorresponds to the energy consumption due to the speed fluctuation forreaching the average speed.

It is reminded that, for an electric vehicle, the energy consumption canbe negative. Indeed, braking may allow energy to be recovered in thebattery.

3) Line Graph Construction

In this step, a line graph of the road network is constructed. In graphtheory, a line graph of a graph G (the road network in the present case)is understood to be a graph representing the adjacency relation betweenthe edges of G. The line graph of a graph can be defined as follows:each vertex of the line graph represents an edge (also called arc) ofgraph G and two vertices of the line graph are adjacent (i.e. connected)if and only if the corresponding edges share a common end in graph G.Thus, the line graph is an equivalent representation of the road networkwhere all the maneuvers are correctly decoupled and distinguished, whichenables precise determination of the energy costs.

For the methods according to the prior art, the road network can bemodelled as a directed graph. Let graph G=(V,A), where V is the set ofall nodes and A is the set of all connections between the nodes, i.e.the arcs. Let w: A→W be a function assigning a weight to each arc of thegraph. In the graphs used for conventional routing, the weightassociated with the arcs represents either the length or the traveltime. For eco-routing, each weight represents the energy consumption fortravelling through the arc.

According to an embodiment of the invention, the objective of this workcan be to design a strategy based solely on statistical and topologicalinformation on the road network, without using any real driving data.This type of information, often incomplete and/or imprecise, isgenerally available on commercial web map services (online services).For each arc iϵA of the graph, it is possible to know the length, theaverage speed of the current traffic v_(i) that depends on the time ofthe day, and the slope of α₁(x) that varies within the arc considered asa function of the position. Furthermore, some web map services provide adegree of importance for each road segment, specifying whether it is ahighway, a major urban road or a secondary urban street. Besides, theposition of some traffic lights can be available.

By means of the method according to the invention, it is possible toconsiderably improve the precision of assessment of the energyconsumption and of the routing navigation, considering the accelerationsinduced by the various speeds in the road segments and/or by the knowninfrastructure elements.

Taking account of the interface accelerations between adjacent arcsposes a problem for modelling the road network as a directed graph(prior art) and particularly for assigning weights to each arc. Inparticular, each node of the graph with two or more incoming arcs iscritical because v_(i 1) and therefore E_(jump,i) are not unique. Ofcourse, this prevents an unambiguous assignment of weights to the arcs.Therefore, directed graph G is not adequate for the proposed energyconsumption model. This ambiguity can be solved using the line graph asthe graph for the proposed routing strategy.

According to an embodiment of the invention, the line graph of the roadnetwork is constructed by carrying out the following steps:

i) constructing a directed graph of said road network with nodes andarcs (also referred to as segments or edges), the nodes of the directedgraph corresponding to the intersections of the road network, and thearcs of the directed graph corresponding to the roads connecting theintersections, and

ii) constructing the line graph of said road network with nodes andarcs, the nodes of the line graph corresponding to the arcs of thedirected graph and the arcs of the line graph corresponding to theadjacency of said arcs of the directed graph.

FIG. 3 illustrates by way of non-limitative example these line graphconstruction steps. Road network RR concerns an intersection between tworoads. The first step consists in constructing directed graph GD fromthe road network. Directed graph GD comprises five nodes N correspondingto the four ends of the roads and to the intersection thereof.Furthermore, directed graph GD comprises eight arcs A connecting thenodes and corresponding to the roads of road network RR. The second stepconsists in constructing line graph GA from directed graph GD. Linegraph GA comprises eight nodes N corresponding to each arc of directedgraph GD. Furthermore, line graph GA comprises twenty arcs Acorresponding to the adjacency of nodes N of directed graph GD.

4) Determination of the Energy Consumption for Each Arc of the LineGraph

In this step, a weight is determined for each arc of the line graph. Theweight corresponds to the energy used by the vehicle on this arc. Thedynamic model of the vehicle is therefore applied for each arc of theline graph, by considering the average speed of the vehicle on this arc,and the acceleration of the vehicle for reaching the average speed. Itis thus possible to know with precision the energy consumption on anarc, which allows to determine an optimal route in terms of energyexpenditure.

Using line graph L(G) as the routing graph allows to assign in a uniqueway the weight to each arc of the graph, by decoupling all the possiblemaneuvers modelled in the original graph G. Each arc of the line graphrepresents a path over two adjacent arcs of directed graph G, andtherefore each arc of line graph L(G) contains information on an arc ofthe original directed graph G and on its upstream arc.

This intrinsic property of the line graph not only allows to correctlyconsider the interface accelerations between adjacent arcs, it alsoallows to model in a more realistic manner the impact of theinfrastructure on the energy consumption. More specifically, accordingto a proposed modelling approach, the energy term that takes account ofthe stops/restarts induced by the infrastructure:

$E_{{jump},i} = {{\int_{0}^{t_{{{jump}\; 1},i}}{\left( {{\overset{\sim}{P}}_{{b\; 1},i} + P_{aux}} \right){dt}}} + {\int_{0}^{t_{{{jump}\; 2},i}}{\left( {{\overset{\sim}{P}}_{{b\; 2},i} + P_{aux}} \right){dt}}}}$

This consideration can be introduced only on the arcs of the line graphthat represent the following situations:

-   -   a traffic light or a stop sign at the junction between an        upstream lower priority road and a downstream higher priority        road. The green waves on the major roads are therefore not        penalized;    -   the upstream and downstream arcs are connected by a maneuver        with a turning angle wider than an adjustable threshold.

The line graph L(G)=(V*,A*) of a graph G has the arcs of graph G as itsnodes, therefore iϵA but also iϵV*. Therefore, let w*: A*→W* be a newfunction of weight assignment to the arcs of the line graph. The weightfor each arc kϵA* is defined as follows:

$W_{k}^{*} = \left\{ \begin{matrix}{{E_{b,i} + E_{{jump},i}},} & {{{{if}\mspace{14mu} i} - 1} \in {V^{*}{\mspace{11mu} \;}{has}\mspace{14mu} {incoming}{\mspace{11mu} \;}{arcs}}} \\{{{\overset{\_}{E}}_{b,i} + E_{{jump},i} + {\overset{\_}{E}}_{b,{i - 1}}},} & {{{{if}\mspace{14mu} i} - 1} \in {V^{*}{\mspace{11mu} \;}{has}\mspace{14mu} {no}\mspace{14mu} {incoming}{\mspace{11mu} \;}{arcs}}}\end{matrix} \right.$

It is reminded that, for an electric vehicle, the energy on an arc canbe negative. Therefore, the weight of this arc of the line graph can benegative. Indeed, braking can allow energy to be recovered in thebattery.

5) Route Determination

In this step, the route minimizing the energy consumption of the vehiclebetween the identified position and the identified destination isdetermined. This step is carried out by taking into account the energyconsumption on each arc of the line graph. Determination of theeco-route is performed by a shortest path algorithm. The shortest pathalgorithm determines the route on the line graph by taking account ofthe energy consumption determined for each arc. The optimum algorithmthat computes the shortest path in a directed and weighted graph from asource vertex is the Bellman-Ford algorithm. The selected algorithm issuited to take account of a negative weight (i.e. energy consumed) on atleast one arc of the line graph, unlike others such as Dijkstra'salgorithm which, although faster, is not optimal in the presence of arcswith negative weights.

Once the algorithm reproduces the optimum sequence of nodes of the linegraph, this result can be readily transferred to the original graph bygenerating the sequence of nodes of the original graph between originand destination corresponding to the optimum path, i.e. the optimumroute in terms of energy expenditure.

According to an embodiment of the invention, the proposed approach cancomprise a stage of offline recording of the global historicalinformation on the traffic conditions of different days of a weekselected at different times of the day. Real-time adaptation isimplemented only after the driver selects the starting point, thedestination and the departure time. The N best eco-routes are computedfrom the historical data. Their total cost is subsequently updatedaccording to the current traffic conditions and compared so as todetermine the best current route in terms of energy consumption. Thissolution allows the traffic conditions to be taken into account in realtime.

Indeed, traffic conditions vary a lot throughout the day and, to reachan optimum global eco-routing solution, the energy cost of all the arcsof the graph should be updated according to the desired departure time.The size of the graph can be large and the computational time forupdating all the weights is not suited for real-time use.

Besides, according to an embodiment of the invention, the computed routecan be compared with other routes obtained using various performanceindices, notably the travel time. Thus, the user can choose, as needed,the most interesting compromise between energy consumption and traveltime.

An optional step of the method according to the invention can consist indisplaying the route determined, for example on the screen of ageolocation system (GPS, Galileo), of a smartphone, on the dashboard ofthe vehicle, on a website, etc. Thus, it is possible to inform the useror any other person (for example a vehicle fleet manager, a roadinfrastructure manager, etc.) of the eco-route. It is also possible todisplay the energy consumption for the route, which is assessed by meansof the model and of the line graph.

The method according to the invention can be used for motor vehicles. Itcan however be used in the field of road transport, two-wheelers, etc.

Furthermore, the invention relates to a computer program productdownloadable from a communication network and/or recorded on acomputer-readable medium and/or processor or server executable. Thisprogram comprises program code instructions for implementing the methodas described above, when the program is executed on a computer or on amobile phone.

Examples

The two examples presented below show the good consistency of thedynamic model according to the invention with measured values. Thedynamic model used for these two examples is the model exemplified inthe application (step 2).

The examples were carried out with an electric vehicle having thecharacteristics shown in Table 1.

TABLE 1 Characteristics of the vehicle Characteristics Symbol Value Massof the vehicle m 1190 kg Wheel radius r 0.2848 m Transmission ratioρ_(t) 5.763 Transmission efficiency η_(t) 0.95 Acceleration a 1.5 m/s²Coefficient a₀ 125.73 N Coefficient a₁ 1.72 N/(m/s) Coefficient a₂ 0.58N/(m/s)² Minimum engine torque T_(m,min) −50 Nm Maximum engine torqueT_(m,max) 200 Nm Electric motor efficiency η_(b) 0.85

The experimental results for these examples were obtained with open roadtests by recording the position and the speed using a GPS sensor. Thetests were carried out in town, on various road types so as to check therobustness and the precision of the consumption prediction by thedynamic model of the method according to the invention. The same routewas used repeatedly, always at the same departure time, for severaldays. The energy consumption subsequently used as the reference wascomputed using the dynamic model described above from the realinstantaneous speed profile recorded. The energy consumption wasassessed by the macroscopic model which is the object of the inventionfrom average traffic speeds obtained by the web (traffic) map services.

Two validation results are presented here. These results illustrate theimprovement of the energy consumption assessment in relation to thestandard technique used in the prior art.

First Case Study

The first validation study was carried out on a route with a combinationof urban roads and highway.

FIG. 4 illustrates, for this first case study, the various speeds Vmes(km/h) measured as a function of the traveled distance D (m) on thispath. FIG. 4 also illustrates the average speed Vmoy on each routesegment. Average speed Vmoy is obtained as a function of the trafficconditions by communication with online services. The real speedprofiles Vmes show good repeatability characteristics even though theycorrespond to different days. The average speed Vmoy macroscopic data isfairly representative of the traffic conditions at the time of thetests.

FIG. 5 illustrates, for this first case study, the cumulative energyconsumption E (Wh) over the distance D (m) traveled on this route. Thisgraph shows the cumulative energy consumption for the measured valuesMES (obtained with the measured speeds), where the cumulative energyconsumption assessed with the average speed with a model according tothe prior art AA does not take account of acceleration, and thecumulative energy consumption assessed with the model according to theinvention INV that takes acceleration into account. The model based onthe average speeds AA that does not take accelerations into accountleads to significant errors by underestimating the true consumption. Theerror of this type of model in relation to the average of the referencefinal energy values in this first case study is approximately 30%. Thedynamic model proposed in the invention INV, which also takes account ofaccelerations, can follow more precisely the consumption variationtrends. The energy consumption assessment error in relation to thereference is approximately 7%.

Second Case Study

The second validation study was carried out on a route with onlysecondary urban roads.

FIG. 6 illustrates, for this second case study, the various speedsmeasured Vmes (km/h) as a function of the traveled distance D (m) onthis path. FIG. 6 also illustrates the average speed Vmoy on each routesegment. Average speed Vmoy is obtained as a function of the trafficconditions by communication with online services. The real speedprofiles Vmes show good repeatability characteristics even though theycorrespond to different days. The average speed Vmoy macroscopic data isfairly representative of the traffic conditions at the time of thetests.

FIG. 7 illustrates, for this second case study, the cumulative energyconsumption E (Wh) over the distance D (m) traveled on this route. Thisgraph shows the cumulative energy consumption for the measured valuesMES (obtained with the measured speeds), where the cumulative energyconsumption assessed with the average speed with a model according tothe prior art AA does not take account of acceleration, and thecumulative energy consumption assessed with the model according to theinvention INV that takes acceleration into account. In this second casestudy, the models based on the average speeds AA according to the priorart that do not take accelerations into account lead to yet moresignificant errors by underestimating the true consumption. The error inrelation to the reference is approximately 38%. This behaviour is due tothe fact that, on secondary urban roads, the precision and thereliability of the macroscopic average speed data are much lower. Thus,the average speeds are less representative of the true trafficconditions, which may also pose problems with the models integratinginterface accelerations. In particular, if the macroscopic data providesaverage speeds that do not vary or hardly vary between the various roadsegments, taking account of the interface accelerations is no longersufficient for correct energy consumption prediction.

That is precisely why the invention also allows to enrich the roadnetwork data by integrating the speed perturbations induced by criticalelements of the road infrastructure.

The dynamic model proposed in the invention can follow more preciselythe consumption variation trends. The energy consumption assessmenterror in relation to the reference is approximately 9%.

1) A method of determining a route minimizing the energy consumption ofa vehicle travelling on a road network (RR), characterized in that thefollowing steps are carried out: a) identifying the position and thedestination of said vehicle, b) constructing a dynamic model (MOD) ofsaid vehicle that relates the energy consumed by said vehicle to thespeed and the acceleration of said vehicle, c) constructing a line graph(GA) of said road network between said identified position of saidvehicle and said identified destination of said vehicle, d) determiningthe energy consumed by said vehicle for each arc of said line graph (GA)by means of said dynamic model (MOD) of the vehicle and of an averagespeed of said vehicle on said considered arc, and of an acceleration ofsaid vehicle to reach said average speed on said considered arc, e)determining said route (ITI) between said identified position of saidvehicle and said identified destination of said vehicle by means of ashortest path algorithm (ALG) minimizing on said line graph (GA) saidenergy consumption, said shortest path algorithm being suited to takeinto account, where appropriate, a negative energy consumption on atleast one arc of said line graph. 2) A method as claimed in claim 1,wherein said average speed and said acceleration of said vehicle aredetermined by means of traffic conditions (TRA) and/or of the topology(TOP) and/or of the infrastructures of said road network. 3) A method asclaimed in claim 2, wherein said traffic conditions (TRA) are obtainedin real time through communication with online data services. 4) Amethod as claimed in claim 2, wherein said traffic conditions (TRA) arestored in historical data storage means. 5) A method as claimed in claim1, wherein the line graph (GA) is constructed using the topology (TOP)of the road network. 6) A method as claimed in claim 2, wherein thetopology (TOP) of the road network (RR) is determined using geolocationmeans. 7) A method as claimed in claim 1, wherein the dynamic model(MOD) of the vehicle depends on intrinsic parameters (PAR) of thevehicle. 8) A method as claimed in claim 7, wherein the intrinsicparameters (PAR) of the vehicle are obtained from a database ortransmitted by a user. 9) A method as claimed in claim 1, wherein theroute (ITI) is displayed on an autonomous device or on the dashboard ofthe vehicle. 10) A method as claimed in claim 1, wherein the dynamicmodel (MOD) of the vehicle depends on the power request of at least oneauxiliary system of the vehicle. 11) A method as claimed in claim 10,wherein the power request of at least one auxiliary system depends onthe outside temperature. 12) A method as claimed in claim 1, wherein theshortest path algorithm (ALG) is a Bellman-Ford algorithm. 13) A methodas claimed in claim 1, wherein the line graph (GA) is constructed bycarrying out the following steps: i) constructing a directed graph (GD)of the road network (RR) with nodes (N) and arcs (A), the nodes (N) ofthe directed graph (GD) corresponding to the intersections of the roadnetwork, and the arcs (A) of the directed graph corresponding to theroads connecting the intersections, and ii) constructing the line graph(GA) of the road network (RR) with nodes (N) and arcs (A), the nodes (N)of the line graph (GA) corresponding to the arcs (A) of the directedgraph (GD) and the arcs (A) of the line graph (GA) corresponding to theadjacency of the arcs (A) of the directed graph (GD). 14) A computerprogram product downloadable from a communication network and/orrecorded on a computer-readable medium and/or processor or serverexecutable, comprising program code instructions for implementing themethod as claimed in claim 1, when the program is executed on a computeror on a mobile phone.